A particle in Electric and Magnetic field

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Homework Help Overview

The discussion revolves around a charge q released in crossed electric (E) and magnetic (B) fields, with E oriented along the y-axis and B oriented about the z-axis. Participants are tasked with deriving the equation of motion for the charge.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriate equations to use, particularly the force equation F = q(E + v × B) and its relation to Newton's second law. Questions arise regarding the meaning of r'' as acceleration and the implications of motion without deflection in the presence of the fields.

Discussion Status

Some participants have offered guidance on writing the electric and magnetic field vectors in component form and determining the force components. There is an ongoing exploration of the implications of the forces involved and the resulting motion.

Contextual Notes

Participants are considering the conditions under which the charge moves without deflection and the resulting forces acting on it. The discussion includes clarifications on the definitions and implications of the variables involved.

Abdul.119
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Homework Statement


A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

Homework Equations

The Attempt at a Solution


I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?
 
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What exactly is r"?
 
Suraj M said:
What exactly is r"?

r is just position, and by r'' I mean it is r derived twice so that it is acceleration
 
Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?
 
Suraj M said:
Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?
In general it should be F = ma
 
What would be the shape of the path of the object?
 
Abdul.119 said:

Homework Statement


A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

Homework Equations

The Attempt at a Solution


I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?
Yes, it is correct.
You know the direction of the electric and magnetic field vectors. Write them out in vector form, and determine the components Fx, Fy, Fz of the force. Note that the force depends on the velocity, that is, (x'x, y'y, z'z) , Then you get three equations in the form mx"=Fx, my"=Fy, mz"=Fz.
 

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